Question

Consider the functions f(x) = x² + x - 6 and g(x) = x + 2. Some students want to determine f(x)/g(x).

Sam states that he must use polynomial long division because it is not possible to use synthetic division for these functions.
Jamal states that it is possible to use either polynomial long division or synthetic division for these functions.
Miguel states that it is not possible to use neither polynomial long division nor synthetic division for these functions.
Which student is correct?
A. Sam
B. Jamal
C. Miguel

Answer 1

Jamal is correct. Both polynomial long division and synthetic division can be used for these functions.

Step-by-step explanation:

The student correct is B. Jamal. Both polynomial long division and synthetic division can be used to find the quotient of f(x) and g(x).To find f(x)/g(x), you can use either method. Synthetic division is a quicker and easier method when dividing by a linear function like g(x) = x + 2. However, polynomial long division can also be used and is a more general method that can be used for any polynomial divisor.

Therefore, Jamal is correct in stating that it is possible to use either polynomial long division or synthetic division for these functions.